Results in Mathematics

, Volume 38, Issue 1–2, pp 152–165 | Cite as

The sets of abstract trigonometric series induced by Lp

  • Jaak Sikk


The constructive character of Lp and the rate-summability provide starting-points for the present investigation. This paper considers the constructive spaces L p and \(\mathcal{L}_{T\lambda }^p\). The constructive character of these spaces is determined by the rate λ. By appropriate λ’s the L p forms the subspaces of Lp and the \(\mathcal{L}_{T\lambda }^p\) forms the abstract sets of Fourier-Schwartz series. The constructive spaces preserve (in generalized form) the structural properties of Lp. It is used to develop the G. Goes method of complementary spaces and to consider the multipliers between different constructive spaces.

1991 Mathematics Subject Classification

40A30 42A24 42A45 

Key words and phrases

trigonometric series summability multipliers 


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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  1. 1.Department of MathematicsEstonian Agricultural UniversityTartuEstonia

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